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Momentum and Impulse

Definition: Linear momentum

$\displaystyle\vec{p}$ = m$\displaystyle\vec{v}$      (1)

We can rewrite Newton's Second Law in terms of momentum:

$\displaystyle\Sigma$$\displaystyle\vec{F}$ = m$\displaystyle\vec{a}$ = m$\displaystyle{\frac{\Delta v}{\Delta t}}$ = $\displaystyle{\frac{\Delta p}{\Delta t}}$.      (2)
Interpretation: Force can be expressed as:
$\displaystyle{\frac{\hbox{the change in momentum}}{\hbox{the time to make the change}}}$.        

Definition: Impulse ( $\vec{I}$ )

$\displaystyle\vec{I}$ = $\displaystyle\vec{F}$$\displaystyle\Delta$t = $\displaystyle\Delta$$\displaystyle\vec{p}$.      (3)
Note: Usually the force is a strongly dependent function of time. In this case, we need to use the average force in the above equation.